N 2009 Tim Gowers – a mathematician at Cambridge University and a recipient of the prestigious Fields Medal – used his blog to invite readers to help him solve a difficult mathematical problem. He dubbed his experiment the Polymath Project.

For seven hours there were no replies. Then a Canadian academic posted a comment, followed by an Arizona high school teacher, then a fellow Fields Medallist from the University of California. Over the next five weeks, twenty-seven people exchanged 800 online comments. They not only cracked the problem; they also solved a more difficult conundrum that included the original as a special case.

The Polymath Project exemplifies the new possibilities of networked science explored by Michael Nielsen in Reinventing Discovery. Nielsen, an expatriate Australian and one-time Federation Fellow at the University of Queensland, has spent most of his career in North America – first as one of the pioneers of quantum computing, and more recently as an advocate of open science. Reinventing Discovery is a manifesto for open science, directed towards breaking the shackles of contemporary scientific culture and the scientific publishing industry.

Nielsen believes that we are on the verge of a new era of scientific discovery facilitated by the internet. Future generations will look back on this era in the same way as we look back on the first scientific revolution of the seventeenth and eighteenth centuries, when organised science transformed human societies. While there is a tension between Nielsen as a chronicler of this transformation and as an advocate of further change, this complicates Reinventing Discovery rather than diminishes it.

The first half of Reinventing Discovery elaborates on how online tools make us smarter. It employs examples such as Microsoft’s online chess match, “Kasparov versus the World,” Linux open-source software and Wikipedia. Nielsen argues that these examples go above and beyond the “wisdom of crowds,” amplifying human intelligence at the limits of human problem-solving ability. (Nielsen has no time for those who argue that the internet reduces our intelligence. This “is like looking at the automobile and concluding it’s a tool for learner drivers to wipe out terrified pedestrians.”)

The key to online tools, Nielsen argues, is making the right connections with the right people at the right time. As it stands, scientific discovery is often constrained by lack of specific expertise, and breakthroughs often depend on fortuitous coincidence. Online tools facilitate “designed serendipity” by creating an “architecture of attention” that directs people’s attention and skills to where they are most needed.

Specifically, effective online tools “modularise” the problem, splitting it into small sub-tasks which can be attacked more or less independently. They encourage small contributions, which reduces barriers to entry and extends the range of available expertise. And they develop a rich “information commons,” allowing people to build on earlier work. Wikipedia provides a neat example of all of these things.

But online tools only work when participants share a body of knowledge and techniques – which Nielsen describes as a “shared praxis.” There are many fields of activity where there is no shared praxis, such as fine arts, politics and the better part of economics. In these circumstances, people are unable to agree on the nature of the problem, and online tools provide no help in scaling up collective intelligence.

Phi Beta Iota: Many of these ideas have been proferred below. The major issue we have with the proposition is that it focuses only on the sciences. As E. O. Wilson argued in CONSILIENCE: The Unity of Knowledge, the sciences need the humanities. Engineering without ethics is like a putting a rapid fire weapon in the hands of a spastic teen-ager. Engineers have allowed their genius to be corrupted both by isolation and by mis-application.